Hi all-
Interested party just wondering if there is any update on this.
Cheers,
Adam
On Tuesday, June 24, 2014 at 10:01:56 AM UTC-7, Aaron Meurer wrote:
A multidimensional version of collect() would probably be the best
abstraction.
Aaron Meurer
On Sun, Jun 15, 2014 at 10:26 AM, James Crist <[email protected]
<javascript:>> wrote:
> We certainly could. The question would then be what the scope of the
method
> should be. Should it only handle systems that can be expressed as Ax =
b? Or
> should it behave like `CoefficientArrays` mentioned above, and handle Ax
+
> Bx^2 + Cx^3 + D = 0? Either way, I think it should error if the form
can't
> be matched exactly (i.e. don't linearize, just express a linear, or
> polynomial, system as matrices).
>
>
> On Saturday, June 14, 2014 6:44:21 PM UTC-5, Aaron Meurer wrote:
>>
>> Oh, of course. B is on the rhs. This is probably more natural to me too.
>>
>> Should we make a convenience function that does this? I think this use
>> of jacobian would be lost on most people.
>>
>> Aaron Meurer
>>
>> On Sat, Jun 14, 2014 at 6:29 PM, James Crist <[email protected]> wrote:
>> > It's just the convention I'm most used to. Systems that can be
expressed
>> > as
>> > A*x = B I usually solve for x, or if A isn't square, the least squares
>> > solution x. In both cases you need A and B in this form. I suppose Ax
+
>> > B
>> > could seem more natural though.
>> >
>> > On Friday, June 13, 2014 6:45:48 PM UTC-5, Aaron Meurer wrote:
>> >>
>> >> That's a clever trick. I should have thought of that.
>> >>
>> >> Is there any reason you let system = A*x - B instead of A*x + B? The
>> >> latter seems more natural.
>> >>
>> >> Aaron Meurer
>> >>
>> >> On Sat, Jun 7, 2014 at 12:28 AM, James Crist <[email protected]> wrote:
>> >> > I just answered this on gitter earlier today, but you can just take
>> >> > the
>> >> > jacobian of the system to get its matrix form. For example:
>> >> >
>> >> > In [1]: from sympy import *
>> >> >
>> >> > In [2]: a, b, c, d = symbols('a, b, c, d')
>> >> >
>> >> > In [3]: x1, x2, x3, x4 = symbols('x1:5')
>> >> >
>> >> > In [4]: x = Matrix([x1, x2, x3, x4])
>> >> >
>> >> > In [5]: system = Matrix([a*x1 + b*x2 + c,
>> >> > ...: c*x1 + d*x3 + 2,
>> >> > ...: c*x3 + b*x4 + a])
>> >> >
>> >> > In [6]: A = system.jacobian(x)
>> >> >
>> >> > In [7]: B = A*x - system
>> >> >
>> >> > In [8]: A
>> >> > Out[8]:
>> >> > Matrix([
>> >> > [a, b, 0, 0],
>> >> > [c, 0, d, 0],
>> >> > [0, 0, c, b]])
>> >> >
>> >> > In [9]: B
>> >> > Out[9]:
>> >> > Matrix([
>> >> > [-c],
>> >> > [-2],
>> >> > [-a]])
>> >> >
>> >> > In [10]: assert A*x - B == system
>> >> >
>> >> > The functionality I'm adding for my GSoC for linearizing a system
of
>> >> > equations will also be able to return these matrices in a
convenient
>> >> > form.
>> >> > But it's not terribly difficult to solve for these arrangements
using
>> >> > the
>> >> > current functionality.
>> >> >
>> >> >
>> >> >
>> >> >
>> >> >
>> >> >
>> >> >
>> >> > On Thursday, June 5, 2014 4:22:52 PM UTC-5, Andrei Berceanu wrote:
>> >> >>
>> >> >> Was this implemented into sympy at any point? It could be the
>> >> >> equivalent
>> >> >> of Mathematica's CoefficientArrays function.
>> >> >>
>> >> >> On Thursday, November 14, 2013 5:56:22 AM UTC+1, Chris Smith
wrote:
>> >> >>>
>> >> >>> I forgot that as_independent, without the as_Add=True flag will
>> >> >>> treat
>> >> >>> Muls differently. The following will be more robust:
>> >> >>>
>> >> >>> def eqs2matrix(eqs, syms, augment=False):
>> >> >>> """
>> >> >>> >>> s
>> >> >>> [x + 2*y == 4, 2*c + y/2 == 0]
>> >> >>> >>> eqs2matrix(s, (x, c))
>> >> >>> (Matrix([
>> >> >>> [1, 0],
>> >> >>> [0, 2]]), Matrix([
>> >> >>> [-2*y + 4],
>> >> >>> [ -y/2]]))
>> >> >>> >>> eqs2matrix([2*c*(x+y)-4],(x, y))
>> >> >>> (Matrix([[2*c, 2*c]]), Matrix([[4]]))
>> >> >>> """
>> >> >>> s = Matrix([si.lhs - si.rhs if isinstance(si, Equality) else
si
>> >> >>> for
>> >> >>> si in eqs])
>> >> >>> sym = syms
>> >> >>> j = s.jacobian(sym)
>> >> >>> rhs = -(s - j*Matrix(sym))
>> >> >>> rhs.simplify()
>> >> >>> if augment:
>> >> >>> j.col_insert(0, rhs)
>> >> >>> else:
>> >> >>> j = (j, rhs)
>> >> >>> return j
>> >> >>>
>> >> > --
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